Posts Tagged ‘Paul Samuelson’

Back in the 1960s there was a famous debate between economists (led by Joan Robinson and Piero Sraffa) of the University of Cambridge in England and economists (led by Paul Samuelson and Robert Solow) of MIT in Cambridge, Massachusetts. The debate, known as “the Cambridge capital controversy“, was over measurement and aggregation of physical capital. The Cambridge (England) economists argued that aggregate physical capital could not be measured without reference to the rate of return on capital. Cambridge (Massachusetts) generally agreed that the Cambridge (England) side won, though many professors of economics continue to teach aggregate production functions and economic growth theory as though the debate never took place.

A similar debate is now taking place, over human rather than physical capital. Noah Smith (HT Mark Thoma) provides a nice overview for those are interested.

Is “human capital” really capital? This is the topic of the latest econ blog debate. Here is Branko Milanovic, who says no, it isn’t. Here is Nick Rowe, who says yes, it is. Here is Paul Krugman, who says no, it isn’t. Here is Tim Worstall, who says yes, it is. Here is Elizabeth Bruenig, who says that people who say it is are bad.

Noah Smith offers an alternative view: human capital requires owners to work (give up leisure time) to obtain a return from it, so the more leisure is valued relative to other things, the less valuable human capital is. This will be different for each person. In consequence, you are “entitled to your own modeling conventions and definition of terms. So whether human capital is capital is up to you.”

This is an interesting, complex debate. I am still thinking about it but, as TdJ readers might predict, I am most persuaded by the arguments of Carleton University economist Nick Rowe. Before turning to Branko Milanovic and Nick Rowe, however, I would like to emphasize two points that are not always appreciated by participants in this debate. First, financial capital is not capital in an economic sense. Nick makes this point clearly, but others confuse financial capital with physical capital. Financial capital – stocks, bonds and the like – are just pieces of paper, IOUs. They are claims of lenders, and the loans may even have been made for the purpose of consumption rather than investment.

Second, even if human capital is a useful category of income-producing assets (and I think it is), it is as difficult to measure as physical capital is. In fact, it is probably even more difficult to measure. This does not really matter though, as it is impossible to measure aggregate assets of either asset apart from (only in theory!) the present value of the future income the assets produce. The problems of measurement of human capital are very similar to the problems of measurement of physical capital. For example, if I purchase an automobile which I use for pleasure, and also – as an Uber driver – to generate income, part of the purchase represents investment (addition to physical capital) and part is consumption. Similarly, part of the expense of schooling represents investment (for the purpose of earning more income than I would without skills) and part is consumption (the satisfaction of obtaining knowledge and the ability to better understand the world in which I live).

There is much, much more at the links above. Bloggers will no doubt continue to debate this issue for weeks and months (years?) to come. Here, to get you started, are brief quotes from Branko Milanovic (on the ”No’ side of the debate, and from Nick Rowe (on the ‘Yes’ side, the one that I support):

If “human capital” and “real” capital are the same thing, how can there be a conflict between labor and capital? If profits and wages are the same thing, why should we fight about distribution? You have your form of capital (which just happens to look like labor), and I have mine, which just happens to look like T-bills and stocks.

This is untrue. Perhaps to my shame, I didn’t even learn of Eugene Fama’s “efficient market hypothesis” (EMH) until a decade after my creation of the 500 Index Fund. Rather, I was inspired by another Nobel laureate, economist Paul Samuelson, who in his 1974 essay in the Journal of Portfolio Management demanded “brute evidence” that active money managers could beat the market index. Such evidence has yet to be produced.

Numbers-crunching economists like Mr. Fama represent the “quantitative school” of indexing who came to believe in stock-market efficiency. In fact, he inspired the founding of Dimensional Fund Advisors (DFA), which follows, not an indexing strategy, but a strategy based on persistent undervaluations of various market segments. Mr. Fama continues to serve on the DFA board.

The “pragmatic school” of indexing, on the other hand, simply amassed vast statistical evidence showing that the returns earned by active managers seldom outpace the S&P 500 Index. Further analysis showed that the failure of active fund managers was a result of the costs they incurred. The average manager is average, but only before all these fund operating expenses, advisory fees, turnover costs and sales loads. After those costs, active management becomes a loser’s game. It is the “cost matters hypothesis” (CMH) that assures that investors in low-cost index funds win the battle for superior returns.

There is more at the link, including a paragraph on another 2013 Nobel laureate, Robert Shiller.

John Bogle (born 1929) founded The Vanguard Group in 1974. Vanguard 500 was the first index fund that the general public was allowed to purchase. Mr Bogle is author of numerous books, including Common Sense on Mutual Funds: New Imperatives for the Intelligent Investor (McGraw-Hill, 1999).

In light of Mr Bogle’s revelation, FT “undercover economist” Tim Harford was wrong to attribute to Eugene Fama ideas that “have helped popularise low-cost, diversified investment and discredit the idea that masters of the financial universe should be richly rewarded for their stockpicking ability”. Paul Samuelson was responsible for this insight and, much later, John Bogle and Robert Shiller for its popularisation.

To his credit, Canadian-born economist and blogger David Henderson apologized for his error.

Thanks for your correction, Mr. Bogle. My apologies for misrepresenting the source of your thinking. Also, thanks for setting up the fund. In my retirement investments, I’ve been a big beneficiary.

The current issue of the Journal of Economic Perspectives (open access) has a 14-page essay on the Cobb-Douglas regression, a popular form of aggregate production function. About time, I thought, that someone writing in a popular journal exposed this work-horse of econometrics for the fraud that it is. I accessed the essay with great anticipation, only to find it full of praise, with very light – almost non-existent – criticism. Here are the essay’s two concluding sentences:

There remain open questions about the scientific value of this procedure in each of the contexts in which it is applied, some of which are variations of the friendly and unfriendly questions raised by Douglas’s initial critics. However, measured by the extent to which it has been embraced, applied, and elaborated upon by subsequent economists, Douglas’s innovative 1927 idea that one could use statistical analysis to uncover meaningful empirical relationships between inputs and outputs, as well as his specific implementation of that idea using the Cobb–Douglas functional form and least squares regression, was an overwhelming success.

Michigan State University economist Jeff Biddle took to heart this advice of MIT economist Franklin Fisher:

[A]ttempts to explain the impossibility of using aggregate production functions in practice are often met with great hostility, even outright anger. To that I say … that the moral is: “Don’t interfere with fairytales if you want to live happily ever after.”

Nowhere does Professor Biddle mention the most damning criticism of aggregate production functions (including the Cobb-Douglas variant): their good fit to empirical data is a statistical artifact – a result of the fact that the functions reflect the accounting identity between the values of inputs and outputs. In other words, aggregate production functions are almost tautologies – true by definition! This was pointed out independently by two Nobel laureates – Paul Samuelson and Herbert Simon – in articles that were published in 1979, and subsequently ignored by virtually everyone. Here are short quotes from each article:

It is a late hour to raise these doubts about the Emperor’s clothes, but ….

Why use the words “production function” for such an accounting-tautology … ?

Empirical data on the Cobb-Douglas and ACMS [Arrow, Chenery, Minhas and Solow] production functions have been alleged to provide substantial support for the classical theory of the firm–so substantial that further testing of that theory, as distinguished from elaboration of its detail, was no longer necessary. An examination of the evidence suggests instead that the observed good fit of these functions to data … are very likely all statistical artifacts. The data say no more than that the value of the product is approximately equal to the wage bill plus the cost of capital services. This interpretation of the statistical findings is plausible for both interindustry cross-sectional studies and time-series studies, the latter for either a single industry or a whole economy. (p. 469)

The current issue of the Journal of Economic Perspectives (free access) contains a Symposium of three articles on “Field Experiments”. University of Chicago economist John List introduces the collection:

Samuelson and Nordhaus (1985) wrote in their introductory economics textbook a quarter-century ago:

The economic world is extremely complicated. There are millions of people and firms, thousands of prices and industries. One possible way of figuring out economic laws in such a setting is by controlled experiments. A controlled experiment takes place when everything else but the item under investigation is held constant. Thus a scientist trying to determine whether saccharine causes cancer in rats will hold “other things equal” and only vary the amount of saccharine. Same air, same light, same type of rat.

Economists have no such luxury when testing economic laws. They cannot perform the controlled experiments of chemists or biologists because they cannot easily control other important factors. Like astronomers or meteorologists, they generally must be content largely to observe.

In my own travels, I have often found similar skepticism. ….

To economists, “field research” has often meant chatting with the cab driver on the way from the airport to another academic seminar. But more and more empirical economists are opening their eyes and searching for situations and questions in which a field experiment might offer a feasible and desirable approach.

As one Climategate e-mailer noted, we do not understand why global warming has paused lately: the models cannot account for it. But this is not for public consumption. …. Just keep saying “flat-earthers” ….

Once scientists are engaged as advocates, science is in trouble. Like intelligence agencies fitting the facts to the policy, they are no longer to be trusted. The IPCC may be serving a righteous cause, but it is not the honest broker this process needs. It has made itself a political agency – at times, a propaganda unit. All this, the public can see.

For the sake of their own credibility, scientists should maintain a cautious distance from politics, and those who take up politics should not expect the deference to disinterested scholars they would otherwise deserve.

Today, two self-explanatory – and rather sad – comments. The first is from an MIT colleague of Paul Samuelson. The second is from an ‘Austrian’ economist.

[A]ttempts to explain the impossibility of using aggregate production functions in practice are often met with great hostility, even outright anger. To that I say … that the moral is: “Don’t interfere with fairytales if you want to live happily ever after.”

Franklin Fisher (1934-) is Professor Emeritus of Microeconomics at MIT.

I don’t see [Paul] Samuelson as someone who traced ideas very deeply or as someone who thought outside the box. I see Samuelson’s technical economics like I see the work of a great chess master. To me, it is questionable whether he contributed to the solution of real economic problems. I admit, however, that I do not know all of Samuelson’s works and you may be able to persuade me otherwise.

I am aware of one sad fact about Samuelson. He apparently knew early on that the “good” econometric results of what became known as neoclassical growth theory using the Cobb-Douglas production function were an artifact. Yet he did not advertise this idea and a generation of lesser minds ended up wasting their time and a generation of textbook writers promoted a false belief he could have easily corrected.

Mr. [Anwar] Shaikh’s article is based on misconception pure and simple. The factor-share device of my 1957 article is in no sense a test of aggregate production functions or marginal productivity or of anything else. It merely shows how one goes about interpreting given time series if one starts by assuming that they were generated from a production function and that the competitive marginal-product relations apply. Therefore, it is not only not surprising but it is exactly the point that if the observed factor shares were exactly constant the method would yield an exact Cobb-Douglas and tuck everything else into the shift factor.

Paul Samuelson became a heretic just five years later, in a critical ‘eulogy’ for a deceased Paul Douglas, co-inventor in 1928 of the Cobb-Douglas Production Function.

Why has the freedom to make h differ from 1 – k been rejected the scatter? Because nature really favors constant returns to scale? Nonsense: she has not shown us her petticoat. Profit and wages add up to total PjQj along any fixed ray not because Euler’s theorem is revealed to apply on that ray but rather because of the accounting identity involved in the residual definition of profit: with PQj a trivial … sum of WLj and RCj along any Lj/Cj ray, how can its form of (WLj)^k (RCj)^h give other than k + h = 1? ….

It is a late hour to raise these doubts about the Emperor’s clothes, but not until undertaking the present assignment did this child give the matter of across- industry fitting the careful attention it deserves and does not seem to have received. ….

Why use the words “production function” for such an accounting-tautology … ?

These words of Paul Samuelson could easily have been written by Herbert Simon, but perhaps not by Joan Robinson. Robert Solow and Paul Samuelson led the American side of the ‘Cambridge controversy’ between Cambridge, England and Cambridge, Massachusetts. Anwar Shaikh taught (and teaches) at the New School University in New York City; he was allied with the Cambridge, England side of the controversy.

Regrettably, no ungated version of Samuelson’s paper is available on the web.

Update:We noted that Herbert Simon’s 1979 paper on production functions has been cited only 67 times. This small number of citations might be attributed to the fact that Simon published his paper in an obscure journal, The Scandinavian Journal of Economics. Well, Samuelson’s 1979 paper was published in the JPE – the leading economics journal – and has received even fewer citations – 38 according to Google Scholar. In contrast, Samuelson’s 1962 paper on the same subject, written when he was a true believer, has been cited 270 times. I conclude that most researchers have not yet lost their faith, so ignore heretical writing.

Some time ago – beginning in July 2007 – I circulated a number of thoughts on production functions to the Thought du Jour list. I have decided to recycle these thoughts, for two reasons. First, to bring them together and make them more accessible, with a single subject line. Second, to reach a larger audience via the blog. The posts might seem a bit wonkish, but none are difficult, I promise. The aggregate production function is the work horse of the economics profession. It is too important a concept to be accepted on faith.

We begin with a quote from Paul Samuelson, one of the most important economists of the twentieth century.

Until the laws of thermodynamics are repealed, I shall continue to relate outputs to inputs — i.e. To believe in production functions.

Paul A. Samuelson, Collected Scientific Papers, 1972, p.174.

I, alas, have lost my faith. Samuelson, we shall see, also lost his in later years.